Recent progress in unitarity techniques for one-loop scattering amplitudes makes a numerical implementation of this method possible. We present a 4-dimensional unitarity method for calculating the cut-constructible part of amplitudes and implement the method in a numerical procedure. Our technique can be applied to any one-loop scattering amplitude and offers the possibility that one-loop calculations can be performed in an automatic fashion, as tree-level amplitudes are currently done. Instead of individual Feynman diagrams, the ingredients for our one-loop evaluation are tree-level amplitudes, which are often already known. To study the practicality of this method we evaluate the cut-constructible part of the 4, 5 and 6 gluon one-loop amplitudes numerically, using the analytically known 4, 5 and 6 gluon tree-level amplitudes. Comparisons with analytic answers are performed to ascertain the numerical accuracy of the method.

Friday, October 05, 2007

Mars et al. make compelling arguments in gr-qc: 0710.0820 that the Universe's accelerated approach towards a future singularity may be due to a change in signature of our braneworld in a bulk 5D Anti de Sitter space (AdS_5).

The authors argue that by choosing hypersurfaces in AdS_5 appropriately, it is possible to construct signature changing branes, with well behaved properties. They explain that hypothetical scientists living on such a hypersurface in AdS_5 might not realize that they are living on a brane, much less a brane that can undergo a Lorentzian -> Euclidean signature change. If the scientists living on the brane use General Relativity as their gravitational theory, they will find that the eigenvalues of the brane Einstein tensor diverge at a 'singularity' placed on the signature changing set. This type of singularity has recently been called a sudden singularity, as well as 'type III' singularity and 'big freeze'. Sudden singularities violate certain energy conditions, signaling the existence of phantom or dark energy components, an illusion caused by an imminent signature change on the brane.

The paper is a nice 8-page read for anyone interested in braneworld cosmology.

Wednesday, October 03, 2007

The relationship between extremal and non-extremal black holes was recently studied by Balbinot et al. in hep-th: 0710.0388. As readers of this blog know, extremal black holes have been all the rage in the string theory community. This is because using D-brane techniques, it is possible to construct an extremal black hole and calculate its entropy. That such D-brane approaches yield an entropy that agrees with the Bekenstein-Hawking formula was hailed as a major triumph for string theory. More recently, Gunaydin and Ferrara have shown that the entropy of black holes in magic supergravities can be calculated using cubic and quartic invariants of the so-called U-duality groups.

Given such success in finding the entropy of extremal black holes, one might wonder why there wasn't more buzz in the popular media. A likely reason is that extremal black holes are rather exotic types of black holes. They have a mass that equals their charge, and are very much unlike the large black holes that astrophysicists rave about. What Balbinot et al. show in their paper is how to continuously transform a non-extremal black hole to an extremal black hole in the limit that mass approaches charge. This was thought to be impossible, as there were arguments that the non-extremal and extremal black holes are distinct quantum mechanical objects.

The arguments in the Balbinot paper are based on a two-dimensional analytical treatment, but the authors argue that their techniques generalize to the four-dimensional case.